ISSN:0075-4102    

DOI:10.1515/crll.1999.509.1

出版商:Walter de Gruyter    

年代:1999

数据来源: Degruyter

摘要:

AbstractLetXbe a nondegenerate integral subscheme of dimension n and degreedin ℙNdefined over the complex number field ℂ.Xis said to bek-regular ifHi(ℙN, ℐX(k – i)) = 0 for alli≧ 1, where ℐXis the sheaf of ideals of ℐℙNand Castelnuovo-Mumford regularity reg(X) ofXis defined as the least suchk. There is a well-known conjecture concerningk-regularity: reg(X) ≦ deg(X) – codim(X) + 1. This regularity conjecture including the classification of borderline examples was verified for integral curves (Castelnuovo, Gruson, Lazarsfeld and Peskine), and an optimal bound was also obtained for smooth surfaces (Pinkham, Lazarsfeld). It will be shown here that reg(X) ≦ deg(X) – 1 for smooth threefoldsXin ℙ5and that the only extremal cases are the rational cubic scroll and the complete intersection of two quadrics. Furthermore, every smooth threefoldXin ℙ5isk-normal for allk≧ deg(X) – 4, which is the optimal bound as the Palatini 3-fold of degree 7 shows. The same bound also holds for smooth regular surfaces in ℙ4other than for the Veronese surface.

ISSN:0075-4102    

DOI:10.1515/crll.1999.509.21

出版商:Walter de Gruyter    

年代:1999

数据来源: Degruyter

ISSN:0075-4102    

DOI:10.1515/crll.1999.509.35

出版商:Walter de Gruyter    

年代:1999

数据来源: Degruyter

ISSN:0075-4102    

DOI:10.1515/crll.1999.509.67

出版商:Walter de Gruyter    

年代:1999

数据来源: Degruyter

ISSN:0075-4102    

DOI:10.1515/crll.1999.509.103

出版商:Walter de Gruyter    

年代:1999

数据来源: Degruyter

摘要:

AbstractWe provide a “toolkit” of basic lemmas for the comparison of homotopy types of homotopy colimits of diagrams of spaces over small categories. We show how this toolkit can be used in quite different fields of applications. We demonstrate this with respect toBjörner's “Generalized Homotopy Complementation Formula” [5],the topology of toric varieties,the study of homotopy types of arrangements of subspaces,the analysis of homotopy types of subgroup complexes.

ISSN:0075-4102    

DOI:10.1515/crll.1999.509.117

出版商:Walter de Gruyter    

年代:1999

数据来源: Degruyter

ISSN:0075-4102    

DOI:10.1515/crll.1999.509.151

出版商:Walter de Gruyter    

年代:1999

数据来源: Degruyter

摘要:

AbstractWe associate Popa systems (= standard invariants of subfactors) to the finite dimensional representations of compact quantum groups. We characterise the systems arising in this way: these are the ones which can be “represented” on finite dimensional Hilbert spaces. This is proved by a universal construction. We explicitely compute (in terms of some free products) the operation of going from representations of compact quantum groups to Popa systems and the back via the universal construction. We prove a Kesten type result for the co-amenability of compact quantum groups, which allows us to compare it with the amenability of subfactors.

ISSN:0075-4102    

DOI:10.1515/crll.1999.509.167

出版商:Walter de Gruyter    

年代:1999

数据来源: Degruyter

摘要:

AbstractGiven an absolutely irreducible Galois representation:GE→ GLN(k),Ea number field,ka finite field of characteristicl>2, and a finite set of placesQofEcontaining all places aboveland ∞ and all where ∞ ramifies, there have been defined many functors representing strict equivalence classes of deformations of such a representation, e.g. by Mazur or Wiles in [15] or [26], with various conditions on the behaviour of the deformations at the places inQand with the condition that the deformations are unramified outsideQ. Those functors are known to be representable. Foras above, our goal is to present a rather general class of global deformation functors that satisfy local deformation conditions and to investigate for those, under what conditions the global deformation functor is determined by the local deformation functors.We will give precise conditions under which the local functors for all places inQare sufficient to describe the global functor, first in a coarse form, then in a refined form using auxiliary primes as done by Taylor and Wiles in [24]. This has several consequences. The strongest is that one can derive ring theoretic results for the universal deformation space by Mazur if one uses results of Diamond and Wiles, cf. [11]and [26], and if one has a good understanding of all local situations. Furthermore it is easier to understand what happens under increasing the ramification as done by Boston and Ramakrishna in [6]and [20], [21]. Finally we shall reinterpret the results in the case of a tame representationby directly considering presentations of certain pro-lGalois groups and revisiting the prime-to-adjoint principle of Boston, cf. [5].

ISSN:0075-4102    

DOI:10.1515/crll.1999.509.199

出版商:Walter de Gruyter    

年代:1999

数据来源: Degruyter